1© Cloudera, Inc. All rights reserved.

LSA-ing Wikipedia with SparkSandy Ryza | Senior Data Scientist

2© Cloudera, Inc. All rights reserved.

Me

• Data scientist at Cloudera

• Recently lead Cloudera’s Apache Spark development

• Author of Advanced Analytics with Spark

3© Cloudera, Inc. All rights reserved.

LSA-ing Wikipedia with SparkSandy Ryza | Senior Data Scientist

4© Cloudera, Inc. All rights reserved.

Latent Semantic Analysis

• Fancy name for applying a matrix decomposition (SVD) to text data

5© Cloudera, Inc. All rights reserved.

6© Cloudera, Inc. All rights reserved.

7© Cloudera, Inc. All rights reserved.

Parse

Raw Data

Clean

Term-Document

MatrixSVD

Interpret Results

8© Cloudera, Inc. All rights reserved.

Parse

Raw Data

Clean

Term-Document

MatrixSVD

Interpret Results

9© Cloudera, Inc. All rights reserved.

Wikipedia Content Data Set

• http://dumps.wikimedia.org/enwiki/latest/• XML-formatted• 46 GB uncompressed

10© Cloudera, Inc. All rights reserved.

<page><title>Anarchism</title><ns>0</ns><id>12</id><revision><id>584215651</id><parentid>584213644</parentid><timestamp>2013-12-02T15:14:01Z</timestamp><contributor><username>AnomieBOT</username><id>7611264</id></contributor><comment>Rescuing orphaned refs (&quot;autogenerated1&quot; from rev584155010; &quot;bbc&quot; from rev 584155010)</comment><text xml:space="preserve">{{Redirect|Anarchist|the fictional character|Anarchist (comics)}}{{Redirect|Anarchists}}{{pp-move-indef}}{{Anarchism sidebar}}

'''Anarchism''' is a [[political philosophy]] that advocates [[stateless society|stateless societies]] often defined as [[self-governance|self-governed]] voluntaryinstitutions,&lt;ref&gt;&quot;ANARCHISM, a social philosophy that rejectsauthoritarian government and maintains that voluntary institutions are best suitedto express man's natural social tendencies.&quot; George Woodcock.&quot;Anarchism&quot; at The Encyclopedia of Philosophy&lt;/ref&gt;&lt;ref&gt;&quot;In a society developed on these lines, the voluntary associations whichalready now begin to cover all the fields of human activity would take a stillgreater extension so as to substitute...

11© Cloudera, Inc. All rights reserved.

Parse

Raw Data

Clean

Term-Document

MatrixSVD

Interpret Results

12© Cloudera, Inc. All rights reserved.

import org.apache.mahout.text.wikipedia.XmlInputFormatimport org.apache.hadoop.conf.Configurationimport org.apache.hadoop.io._

val path = "hdfs:///user/ds/wikidump.xml"val conf = new Configuration()conf.set(XmlInputFormat.START_TAG_KEY, "<page>")conf.set(XmlInputFormat.END_TAG_KEY, "</page>")val kvs = sc.newAPIHadoopFile(path, classOf[XmlInputFormat], classOf[LongWritable], classOf[Text], conf)val rawXmls = kvs.map(p => p._2.toString)

13© Cloudera, Inc. All rights reserved.

Parse

Raw Data

Clean

Term-Document

MatrixSVD

Interpret Results

14© Cloudera, Inc. All rights reserved.

Lemmatization

“the boy’s cars are different colors”

“the boy car be different color”

15© Cloudera, Inc. All rights reserved.

CoreNLP

def createNLPPipeline(): StanfordCoreNLP = { val props = new Properties() props.put("annotators", "tokenize, ssplit, pos, lemma") new StanfordCoreNLP(props)}

16© Cloudera, Inc. All rights reserved.

Stop Words

“the boy car be different color”

“boy car different color”

17© Cloudera, Inc. All rights reserved.

Parse

Raw Data

Clean

Term-Document

MatrixSVD

Interpret Results

18© Cloudera, Inc. All rights reserved.

Tail Monkey Algorithm Scala

Document 1 1.5 1.8

Document 2 2.0 4.3

Document 3 1.4 6.7

Document 4 1.6

Document 5 1.2

Term-Document Matrix

19© Cloudera, Inc. All rights reserved.

tf-idf

• (Term Frequency) * (Inverse Document Frequency)

• tf(document, word) = # times word appears in document

• idf(word) = 1 / (# documents that contain word)

20© Cloudera, Inc. All rights reserved.

val rowVectors: RDD[Vector] = ...

21© Cloudera, Inc. All rights reserved.

Parse

Raw Data

Clean

Term-Document

MatrixSVD

Interpret Results

22© Cloudera, Inc. All rights reserved.

Singular Value Decomposition

• Factors matrix into the product of three matrices: U, S, and V• m = # documents• n = # terms• U is m x n• S is n x n• V is n x n

23© Cloudera, Inc. All rights reserved.

Low Rank Approximation

• Account for synonymy by condensing related terms.• Account for polysemy by placing less weight on terms that have multiple meanings.• Throw out noise.

SVD can find the rank-k approximation that has the lowest Frobenius distance from the original matrix.

24© Cloudera, Inc. All rights reserved.

Singular Value Decomposition

• Factors matrix into the product of three matrices: U, S, and V• m = # documents• n = # terms• k = # concepts• U is m x n• S is k x k• V is k x n

25© Cloudera, Inc. All rights reserved.

Docs:

Terms:U S V

26© Cloudera, Inc. All rights reserved.

Docs:

Terms:U S V

27© Cloudera, Inc. All rights reserved.

rowVectors.cache()val mat = new RowMatrix(rowVectors)val k = 1000val svd = mat.computeSVD(k, computeU=true)

28© Cloudera, Inc. All rights reserved.

Parse

Raw Data

Clean

Term-Document

MatrixSVD

Interpret Results

29© Cloudera, Inc. All rights reserved.

What are the top “concepts”?

I.e. what dimensions in term-space and document-space explain most of the variance of the data?

30© Cloudera, Inc. All rights reserved.

Docs:

Terms:U S V

31© Cloudera, Inc. All rights reserved.

U S V

32© Cloudera, Inc. All rights reserved.

U S V

33© Cloudera, Inc. All rights reserved.

def topTermsInConcept(concept: Int, numTerms: Int) : Seq[(String, Double)] = { val v = svd.V.toBreezeMatrix val termWeights = v(::, k).toArray.zipWithIndex val sorted = termWeights.sortBy(-_._1) sorted.take(numTerms)}

34© Cloudera, Inc. All rights reserved.

def topDocsInConcept(concept: Int, numDocs: Int) : Seq[Seq[(String, Double)]] = { val u = svd.U val docWeights = u.rows.map(_.toArray(concept)).zipWithUniqueId() docWeights.top(numDocs)}

35© Cloudera, Inc. All rights reserved.

Concept 1

Terms: department, commune, communes, insee, france, see, also,

southwestern, oise, marne, moselle, manche, eure, aisne, isère

Docs: Communes in France, Saint-Mard, Meurthe-et-Moselle,

Saint-Firmin, Meurthe-et-Moselle, Saint-Clément, Meurthe-et-Moselle,

Saint-Sardos, Lot-et-Garonne, Saint-Urcisse, Lot-et-Garonne, Saint-Sernin,

Lot-et-Garonne, Saint-Robert, Lot-et-Garonne, Saint-Léon, Lot-et-Garonne,

Saint-Astier, Lot-et-Garonne

36© Cloudera, Inc. All rights reserved.

Concept 2

Terms: genus, species, moth, family, lepidoptera, beetle, bulbophyllum,

snail, database, natural, find, geometridae, reference, museum, noctuidae

Docs: Chelonia (genus), Palea (genus), Argiope (genus), Sphingini,

Cribrilinidae, Tahla (genus), Gigartinales, Parapodia (genus),

Alpina (moth), Arycanda (moth)

37© Cloudera, Inc. All rights reserved.

Querying

• Given a set of terms, find the closest documents in the latent space

38© Cloudera, Inc. All rights reserved.

Reconstructed Matrix(U * S * V)

Doc

Term

39© Cloudera, Inc. All rights reserved.

def topTermsForTerm( normalizedVS: BDenseMatrix[Double], termId: Int): Seq[(Double, Int)] = { val rowVec = new BDenseVector[Double](row(normalizedVS, termId).toArray) val termScores = (normalizedVS * rowVec).toArray.zipWithIndex termScores.sortBy(- _._1).take(10)}

val VS = multiplyByDiagonalMatrix(svd.V, svd.s)val normalizedVS = rowsNormalized(VS)topTermsForTerm(normalizedVS, id, termIds)

40© Cloudera, Inc. All rights reserved.

printRelevantTerms("radiohead")

radiohead 0.9999999999999993

lyrically 0.8837403315233519

catchy 0.8780717902060333

riff 0.861326571452104

lyricsthe 0.8460798060853993

lyric 0.8434937575368959

upbeat 0.8410212279939793

Term Similarity

41© Cloudera, Inc. All rights reserved.

printRelevantTerms("algorithm")

algorithm 1.000000000000002

heuristic 0.8773199836391916

compute 0.8561015487853708

constraint 0.8370707630657652

optimization 0.8331940333186296

complexity 0.823738607119692

algorithmic 0.8227315888559854

Term Similarity

42© Cloudera, Inc. All rights reserved.

(algorithm,1.000000000000002), (heuristic,0.8773199836391916),

(compute,0.8561015487853708), (constraint,0.8370707630657652),

(optimization,0.8331940333186296), (complexity,0.823738607119692),

(algorithmic,0.8227315888559854), (iterative,0.822364922633442),

(recursive,0.8176921180556759), (minimization,0.8160188481409465)

43© Cloudera, Inc. All rights reserved.

def topDocsForTerm(US: RowMatrix, V: Matrix, termId: Int) : Seq[(Double, Long)] = { val rowArr = row(V, termId).toArray val rowVec = Matrices.dense(termRowArr.length, 1, termRowArr) val docScores = US.multiply(termRowVec) val allDocWeights = docScores.rows.map( _.toArray(0)). zipWithUniqueId() allDocWeights.top( 10)}

44© Cloudera, Inc. All rights reserved.

printRelevantDocs("fir")

Silver tree 0.006292909647173194

See the forest for the trees 0.004785047583508223

Eucalyptus tree 0.004592837783089319

Sequoia tree 0.004497446632469554

Willow tree 0.004429936059594164

Coniferous tree 0.004381572286629475

Tulip Tree 0.004374705020233878

Document Similarity

45© Cloudera, Inc. All rights reserved.

• https://github.com/sryza/aas/tree/master/ch06-lsa• https://spark.apache.org/docs/latest/mllib-dimensionality-reduction.html•

More detail?

46© Cloudera, Inc. All rights reserved.

Thank you@sandysifting